Can somebody me with this? explain why the binomial (x + 2) is a factor of this polynomial expression. explain why the binomial (x + 1) is not a factor of this polynomial expression.

We are given polynomial: .

We need to explain why the binomial (x + 2) IS a factor of this polynomial expression and  why the binomial (x + 1) IS NOT a factor of this polynomial expression.

Let us set first factor equal to 0 and solve for x.

x+2=0

x=-2.

Plugging x=-2 in given polynomial, we get

Because x=-2 gives 0 on plugging in given polynomial, so it's factor of given polynomial expression.

Now, let us check second factor x+1=0

x=-1.

Plugging x=-1 in given polynomial, we get

=-5+8+7-6.

= -4.

Because x=-1 doesn't gives 0 on plugging in given polynomial, so it's not a factor of given polynomial expression.